Express your answer as a mixed number simplified to lowest terms. $7\dfrac{2}{12}-3\dfrac{3}{9} = {?}$
Solution: Simplify each fraction. $= {7\dfrac{1}{6}} - {3\dfrac{1}{3}}$ Find a common denominator for the fractions: $= {7\dfrac{1}{6}}-{3\dfrac{2}{6}}$ Convert ${7\dfrac{1}{6}}$ to ${6 + \dfrac{6}{6} + \dfrac{1}{6}}$ So the problem becomes: ${6\dfrac{7}{6}}-{3\dfrac{2}{6}}$ Separate the whole numbers from the fractional parts: $= {6} + {\dfrac{7}{6}} - {3} - {\dfrac{2}{6}}$ Bring the whole numbers together and the fractions together: $= {6} - {3} + {\dfrac{7}{6}} - {\dfrac{2}{6}}$ Subtract the whole numbers: $=3 + {\dfrac{7}{6}} - {\dfrac{2}{6}}$ Subtract the fractions: $= 3+\dfrac{5}{6}$ Combine the whole and fractional parts into a mixed number: $= 3\dfrac{5}{6}$